According to The Journal, the SEC is also looking into why Musk's first statement about the potential of taking Tesla private was made on Twitter instead of in a regulatory filing. The agency also asked the company whether it believes Musk's tweet follows SEC rules about protecting investors, the report said.

Bloomberg reported that the agency had already been gathering information about statements Tesla has made regarding sales and manufacturing targets.

An inquiry from the SEC does not necessarily mean an investigation will follow.

James Rosener, a partner at the law firm Pepper Hamilton, told Business Insider that Twitter was not the right medium for a securities disclosure since the platform's 280-character limit prevented Musk from disclosing enough information relevant to investors — including the structure of the deal, its tax impact, and the amount of debt it would require — to ensure he's not misleading them.

According to Rosener, Musk's tweet likely ran afoul of the SEC's anti-fraud rules.

"There's definitely material omissions," Rosener said. "Clearly, it was not what any lawyer with any experience in this kind of stuff would advise to put out."

David Whiston, an equity strategist at Morningstar who covers the US auto industry, said he was confused by Musk's tweets, which he said indicated Musk had both the funding and the shareholder votes necessary to take the company private.

"I'm still trying to understand why he even went public like this," Whiston said, "because I don't see a point in going public to say you are considering going private unless you're trying to get, perhaps, the price higher than $420 a share, or you're just really eager to hurt the short-sellers. Otherwise, why wouldn't you just wait until you're definitely doing a deal to say something?"

Tesla's board released a statement on Wednesday morning, but it was very brief and offered few details besides that Musk met with the board last week to bring up the possibility of going private. Musk said via Twitter on Tuesday that the deal was contingent on a shareholder vote but that "investor support is confirmed."

According to Probes Reporter, a research firm focusing on undisclosed SEC investigations, the SEC investigated Tesla from June 2016 to May 2017 regarding the Model 3 sedan. Tesla did not disclose the investigation, which did not result in an enforcement action, the firm said.

"I wish we could be private with Tesla," Musk said in an interview with Rolling Stone published in November. "It actually makes us less efficient to be a public company."

Musk has also said on multiple occasions that Tesla will become profitable by the end of this year and won't need to raise additional funds, despite its increased cash-burn rate in recent quarters.

At the end of June, Tesla said it achieved its goal of making 5,000 Model 3s in one week. Musk previously said that the company would hit that number by the end of 2017 and that sustaining such a production rate is critical for Tesla to become profitable.